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The extended F-expansion method and its application for a class of nonlinear evolution equations

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  • Abdou, M.A.

Abstract

By means of a simple transformation technique, we have shown that the higher-order nonlinear Schrödinger equation in nonlinear optical fibers, a new Hamiltonian amplitude equation, generalized Hirota–Satsuma coupled system and generalized ZK-BBM equation can be reduced to the elliptic-like equation. Then, the extended F-expansion method is used to obtain a series of solutions including the single and the combined nondegenerative Jacobi elliptic function solutions and their degenerative solutions to the above mentioned class of nonlinear evolution equations.

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  • Abdou, M.A., 2007. "The extended F-expansion method and its application for a class of nonlinear evolution equations," Chaos, Solitons & Fractals, Elsevier, vol. 31(1), pages 95-104.
    • Handle: RePEc:eee:chsofr:v:31:y:2007:i:1:p:95-104
    DOI: 10.1016/j.chaos.2005.09.030
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    Cited by:

    1. Estévez, P.G. & Kuru, Ş. & Negro, J. & Nieto, L.M., 2009. "Travelling wave solutions of the generalized Benjamin–Bona–Mahony equation," Chaos, Solitons & Fractals, Elsevier, vol. 40(4), pages 2031-2040.
    2. Ye, Caier & Zhang, Weiguo, 2011. "New explicit solutions for (2+1)-dimensional soliton equation," Chaos, Solitons & Fractals, Elsevier, vol. 44(12), pages 1063-1069.
    3. Bekir, Ahmet & Boz, Ahmet, 2009. "Application of Exp-function method for (2+1)-dimensional nonlinear evolution equations," Chaos, Solitons & Fractals, Elsevier, vol. 40(1), pages 458-465.
    4. Ma, Wen-Xiu & Lee, Jyh-Hao, 2009. "A transformed rational function method and exact solutions to the 3+1 dimensional Jimbo–Miwa equation," Chaos, Solitons & Fractals, Elsevier, vol. 42(3), pages 1356-1363.
    5. Seadawy, Aly R. & Ali, Asghar & Althobaiti, Saad & Sayed, Samy, 2021. "Propagation of wave solutions of nonlinear Heisenberg ferromagnetic spin chain and Vakhnenko dynamical equations arising in nonlinear water wave models," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).
    6. Feiyun Pei & Guojiang Wu & Yong Guo, 2023. "Construction of Infinite Series Exact Solitary Wave Solution of the KPI Equation via an Auxiliary Equation Method," Mathematics, MDPI, vol. 11(6), pages 1-25, March.
    7. Han, Tianyong & Li, Zhao & Li, Chenyu, 2023. "Bifurcation analysis, stationary optical solitons and exact solutions for generalized nonlinear Schrödinger equation with nonlinear chromatic dispersion and quintuple power-law of refractive index in ," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 615(C).
    8. Wafaa B. Rabie & Hamdy M. Ahmed & Walid Hamdy, 2023. "Exploration of New Optical Solitons in Magneto-Optical Waveguide with Coupled System of Nonlinear Biswas–Milovic Equation via Kudryashov’s Law Using Extended F-Expansion Method," Mathematics, MDPI, vol. 11(2), pages 1-28, January.
    9. Nur Alam & Fethi Bin Muhammad Belgacem, 2016. "Microtubules Nonlinear Models Dynamics Investigations through the exp(−Φ(ξ))-Expansion Method Implementation," Mathematics, MDPI, vol. 4(1), pages 1-13, February.
    10. Erbaş, Barış & Yusufoğlu, Elçin, 2009. "Exp-function method for constructing exact solutions of Sharma–Tasso–Olver equation," Chaos, Solitons & Fractals, Elsevier, vol. 41(5), pages 2326-2330.
    11. Verma, Pallavi & Kaur, Lakhveer, 2019. "Integrability, bilinearization and analytic study of new form of (3+1)-dimensional B-type Kadomstev–Petviashvili (BKP)- Boussinesq equation," Applied Mathematics and Computation, Elsevier, vol. 346(C), pages 879-886.
    12. Jang, Bongsoo, 2009. "New exact travelling wave solutions of nonlinear Klein–Gordon equations," Chaos, Solitons & Fractals, Elsevier, vol. 41(2), pages 646-654.
    13. Velasco-Juan, M. & Fujioka, J., 2020. "Integral complex modified Korteweg-de Vries (Icm-KdV) equations," Chaos, Solitons & Fractals, Elsevier, vol. 134(C).

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